Related papers: An Elementary Proof for the Basel Problem
By doing a slight change to a beautiful and widely unknown argument by E. L. Stark [E. L. Stark, Application of a Mean Value Theorem for Integrals to Series Summation, Amer. Math. Monthly 85 (1978) 481--483.] we get a candidate to be…
Some time ago Wastlund reformulated the Basel problem in terms of a physical system using the proportionality of the apparent brightness of a star to the inverse square of its distance. Inspired by this approach, we give another physical…
Euler's solution in 1734 of the Basel problem, which asks for a closed form expression for the sum of the reciprocals of all perfect squares, is one of the most celebrated results of mathematical analysis. In the modern era, numerous proofs…
We give a remarkably elementary proof of the Brouwer fixed point theorem. The proof is verifiable for most of the mathematicians.
The Basel problem consists in finding the sum of the reciprocals of the squares of the positive integers. It was finally solved in 1735 by Leonhard Euler. In this paper, we propose a simple proof based on the Weierstrass Sine product…
Bell's theorem is a fundamental result in quantum mechanics: it discriminates between quantum mechanics and all theories where probabilities in measurement results arise from the ignorance of pre-existing local properties. We give an…
Because of its relation to the distribution of prime numbers, the Riemann zeta function {\zeta} (s) is one of the most important functions in mathematics. The zeta function is defined by the following formula for any complex number s with…
The number $\frac{\pi ^{2}}{6}$ is involved in the variance of several distributions in statistics. At the same time it holds $\sum\nolimits_{k=1}^{\infty }k^{-2}= \frac{\pi ^{2}}{6}$, which solves the famous Basel problem. We first provide…
In this article, we provide a new elementary proof of the Basel problem.
We give an elementary proof to Hasse theorem.
An elementary proof of Bertrand's theorem is given by examining the radial orbit equation, without needing to solve complicated equations or integrals.
We give a simple direct proof of Fermat's two squares theorem. Our argument uses no intricate notions or ideas; one might say that it is a proof by careful bookkeeping. As such, the proof may be particularly easy to comprehend by students…
This article provides a simple proof of the quadratic formula, which also produces an efficient and natural method for solving general quadratic equations. The derivation is computationally light and conceptually natural, and has the…
The aim of this short note is to present an elementary, self-contained, and direct proof for the classical Lebesgue decomposition theorem.
We announce here that Fermat's Last theorem was solved, but there is an easy proof of it on the basis of elemetary undergraduate mathematics. We shall disclose such an easy proof.
Most of the assertions in the theory of well ordered sets are quite simple. However, one of its central statements, Zermelo's theorem, stands out of this rule, for its well-known proofs are rather complicated. The aim of the current paper…
We illustrate the concept of mathematical proof.
We prove the Aharoni Berger Conjecture
Arguably the simplest variation of this style of proof as we avoid reducing to the cubic case entirely.
We present a simple short proof of the Fundamental Theorem of Algebra, without complex analysis and with a minimal use of topology. It can be taught in a first year calculus class.